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Nonlinear approximations to problems with mixed boundary conditions are useful for predicting large-scale streaming velocities from the density field, or vice-versa. We evaluate the schemes of Bernardeau \cite{bernardeau92}, Gramann…

Astrophysics · Physics 2007-05-23 Paul J. Mancinelli , Amos Yahil , Galit Ganon , Avishai Dekel

We point out that a special case of an ideal gas exhibits concentration of the volume of its phase space, which is a sphere, around its equator in the thermodynamic limit. The rate of approach to the thermodynamic limit is determined. Our…

Statistical Mechanics · Physics 2015-05-13 Anthony J. Creaco , Nikos Kalogeropoulos

We establish that the optimal bound for the size of the smallest integral solution of the Oppenheim Diophantine approximation problem $\abs{Q(x)-\xi}< \epsilon$ for a generic ternary form $Q$ is $\abs{x}\ll \epsilon^{-1}$. We also establish…

Number Theory · Mathematics 2018-01-04 Anish Ghosh , Alexander Gorodnik , Amos Nevo

A sphere is a fundamental geometric object widely used in (computer aided) geometric design. It possesses rational parameterizations but no parametric polynomial parameterization exists. The present study provides an approach to the optimal…

Numerical Analysis · Mathematics 2021-04-27 Aleš Vavpetič , Emil Žagar

Following on from the second release of calibrated photometry from IPHAS, the INT/WFC Photometric H-alpha Survey of the Northern Galactic Plane, we present incompleteness-corrected stellar density maps in the r and i photometric bands.…

Astrophysics of Galaxies · Physics 2016-01-27 H. J. Farnhill , J. E. Drew , G. Barentsen , E. A. González-Solares

This work is concerned with the study of asymptotic properties of nonparametric density estimates in the framework of circular data. The estimation procedure here applied is based on wavelet thresholding methods: the wavelets used are the…

Statistics Theory · Mathematics 2016-03-16 Claudio Durastanti

Entropic optimal transport offers a computationally tractable approximation to the classical problem. In this note, we study the approximation rate of the entropic optimal transport map (in approaching the Brenier map) when the…

Probability · Mathematics 2024-11-22 Ritwik Sadhu , Ziv Goldfeld , Kengo Kato

Parametric scaling representations are obtained and studied for the asymptotic behavior of interfacial tensions in the \textit{full} neighborhood of a fluid (or Ising-type) critical endpoint, i.e., as a function \textit{both} of temperature…

Statistical Mechanics · Physics 2009-11-10 Shun-yong Zinn , Michael E. Fisher

We study cylindrically symmetric steady-state accretion of polytropic test matter spiraling onto the symmetry axis in power-law and logarithmic potentials. The model allows one to qualitatively understand the accretion process in a symmetry…

High Energy Astrophysical Phenomena · Physics 2019-11-11 Łukasz Bratek , Joanna Jałocha , Marek Kutschera

We propose a numerical method to approximate the scattering amplitudes for the elasticity system with a non-constant matrix potential in dimensions $d=2$ and $3$. This requires to approximate first the scattering field, for some incident…

Numerical Analysis · Mathematics 2021-07-27 Juan A. Barceló , Carlos Castro

Useful approximation formulae for radiation impedance are given for the reflection coefficients of both infinitely flanged and unflanged rigid-walled cylindrical ducts. The expressions guarantee that simple but necessary physical and…

Classical Physics · Physics 2009-10-15 Fabrice Silva , Philippe Guillemain , Jean Kergomard , Bastien Mallaroni , Andrew N. Norris

New exact interior solutions to the Einstein field equations for anisotropic spheres are found. We utilise a procedure that necessitates a choice for the energy density and the radial pressure. This class contains the constant density model…

General Relativity and Quantum Cosmology · Physics 2009-11-11 M. Chaisi , S. D. Maharaj

We study exact solutions of the Einstein-Maxwell equations for the interior gravitational field of static spherically symmetric charged compact spheres. The spheres consist of an anisotropic fluid with a charge distribution that gives rise…

General Relativity and Quantum Cosmology · Physics 2022-02-18 Krsna Dev

To tackle difficulties for theoretical studies in situations involving nonsmooth functions, we propose a sequence of infinitely differentiable functions to approximate the nonsmooth function under consideration. A rate of approximation is…

Econometrics · Economics 2023-09-29 Chaohua Dong , Jiti Gao , Bin Peng , Yundong Tu

We briefly review analytic approximations of thermodynamic functions of fully ionized nonideal electron-ion plasmas, applicable in a wide range of plasma parameters, including the domains of nondegenerate and degenerate, nonrelativistic and…

Plasma Physics · Physics 2010-02-01 A. Y. Potekhin , G. Chabrier

We study a nonlocal diffusion equation of porous medium type featuring a generalised fractional pressure with spatial anisotropy. We construct a finite element method for the numerical solution of the equation on a bounded open Lipschitz…

Numerical Analysis · Mathematics 2026-04-15 Stefano Fronzoni

In this paper, we study an insulation problem that seeks the optimal distribution of a fixed amount $m>0$ of insulating material coating an insulated boundary $\Gamma_I\subseteq \partial\Omega$ of a thermally conducting body…

Analysis of PDEs · Mathematics 2025-08-04 Harbir Antil , Alex Kaltenbach , Keegan L. A. Kirk

We consider the existence of radially symmetric stationary solutions of the compressible viscous and heat-conductive polytropic ideal fluid on the unbounded exterior domain of a sphere where the boundary and far-field conditions are…

Analysis of PDEs · Mathematics 2025-07-08 Itsukoo Hashimoto , Akitaka Matsumura

This article deals with the numerical approximation of effective coefficients in stochastic homogenization of discrete linear elliptic equations. The originality of this work is the use of a well-known abstract spectral representation…

Probability · Mathematics 2010-08-20 Antoine Gloria , Jean-Christophe Mourrat

The one-dimensional Ising model with nearest neighbour interactions and the zero-temperature dynamics recently considered by Lefevre and Dean -J. Phys. A: Math. Gen. {\bf 34}, L213 (2001)- is investigated. By introducing a particle-hole…

Statistical Mechanics · Physics 2009-11-07 A. Prados , J. Javier Brey